Tyrone Ghaswala, Pure Mathematics, University of Waterloo
"Making your stomach Chern"
Consider
a
complex
vector
bundle
$E$
over
a
manifold
$M$.
The
Chern
classes
of
$E$
are
elements
of
the
de
Rham
cohomology
of
$M$,
which
'measure'
how
nontrivial
$E$
is.
We
will
define
these
using
connections,
establish
their
basic
functorial
properties,
and
explicitly
calculate
them
for
$\mathcal
O(n)$
and
$T\mathbb{C}\mathbb{P}^n$.
This
calculation
will
involve
an
object
called
the
Euler
Sequence.